Suppose you have a random process x(t), that is generated from time indexed densities N(m1(t),sigma1(t)) with probability alpha, and from density N(m2(t),sigma2(t)) with probability 1-alpha.The process x(t) is directly unobservable but can be observed through y(t)=f(x(t))+noiseGiven only the data y(t), we develop a methodology to estimate the parameters [m1(t),sigma1(t),m2(t),sigama2(t),alpha] that govern this specified process.We illustrate the application of this methodology using the following processx(t) = a*x(t-1)+Jump(t) where Jump(t)=N(m1,sigma1) with prob. alpha, and Jump(t)=0 with prob. 1-alphay(t) = c*exp(x(t)) + noise;This model was developed because it can be use to generate Random Walks, AR(1) processess, Mean Reversion Processes, Stochastic Volatility, and Stochastics processes with spikes or Jumps. Our particular interest was in developing a model for estimating price spikes in electricity.The paper attached 'An estimation Technique for Time Indexed Gaussian Mixture Model', shows how to develop the estimation procedure for this model and the same technique can be applied to any model of the formx(t)=f(x(t))+Jump(t)y(t)=g(x(t))+noiseThe code attached illustrates the application of our methodology, if is extremely computionally intensive as it requires the use of particle smoothing. This is the extension of the first parameter estimation code, in which we assumed that both (y(t) and x(t)) were known. Now we only assume the data y(t) as given.Run simulationexample.m to obtain 'figure 5' and dataexample.m to obtain 'figure 6'

Communication
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1D infinite Gaussian mixture model 1.0
This is a little script which was designed for educational purposes. It runs out of the box and generates a random data set of 1D Gaussian mixtures and visualizes the inference process.References:* Carl Edward Rasmussen: The infinite Gaussian...

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Development Tools
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EM algorithm for Gaussian mixture model 1.0
This is a function performs maximum likelihood estimation of Gaussian mixture model by using expectation maximization algorithm.It can work on data of arbitrary dimensions. Several techniques are applied in order to avoid the float number...

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gaussian_mixture_model.m 1.0
A Gaussian mixture model means that each data point is drawn (randomly) from one of C classes of data, with probability p_i of being drawn from class i, and each class is distributed as a Gaussian with mean standard deviation mu_i and sigma_i....

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gaussianPlume 1.0
gaussianPlume Steady-state gaussian plume distribution model gaussianPlume models the dispersion of a continuous point source, i.e. plume, in various conditions and terrains. The output of gaussianPlume is a 3-dimensional matrix containing the...

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Peak Interpolation 1.0
Sometimes it is important to be able to estimate the peak of a sampled continuous function between the samples. This is called subsample peak interpolation and is used in radar, delay estimation, and communication. Typically one fits a model to...

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IrisMVC 2.0 rc1
IrisMVC is an OOP PHP framework that developers can use as a strong and secure foundation to build on various web applications following the Model-View-Controller (MVC) pattern. It provides the basic functionality developers need, without...

Development Tools
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Barnardextest 1.0
This file, as the Fisher's exact test, performs the exact probability test for a table of frequency data cross-classified according to two categorical variables, each of which has two levels or subcategories (2x2). It is a non-parametric...